Handling Imbalance in FIE

Statement of Principles of Ratemaking

The Casualty Actuarial Society (CAS) Statement of Principles of Ratemaking outlines four fundamental principles to evaluate whether a rate is actuarially sound:

Principle 1: A rate is an estimate of the expected value of future costs. $\text{Rate} = E(\text{Future Costs})$
Principle 2: A rate provides for all costs associated with the transfer of risk.
Principle 3: A rate provides for the costs associated with an individual risk transfer.
Principle 4: A rate is reasonable, not excessive, not inadequate, and not unfairly discriminatory.

Key Considerations in Ratemaking

To establish actuarially sound rates, several key considerations must be addressed:

Relevance: Use data that is relevant to predicting future costs.
Homogeneity and Reliability: Subdivide data into groups that are sufficiently homogeneous and have a statistically reliable volume.
Credibility: The credibility of the data is a function of its homogeneity and reliability: $\text{Credibility} = f(\text{Homogeneity, Reliability})$
Reinsurance Costs: Incorporate the cost of reinsurance.
Historical vs. Future Conditions: Reflect all internal and external changes when projecting historical data to the future period.
Risk and Profit: Higher-risk coverages require a higher profit charge, and investment income should be reflected.
Documentation: Actuarial judgments should be well-documented and available for disclosure.

Ratemaking Pricing Methods

Various methods can be used to set rates, depending on data availability:

Guessing / Intuition
Non-insurance Data
Competitor Rates
Industry Data
Adjusting Historical Experience (Most Common): Adjusting the insurer’s own historical loss ratios (LR) or pure premiums (PP) to reflect the future period.

Adjustments to Historical Data

To project historical experience to the future prospective period, actuaries must apply several adjustments:

Large Events: Adjust for shock losses or catastrophes.
One-Time Changes: Account for shifts such as benefit level changes or law changes.
Trending: Project premiums, losses, and expenses for inflation and other time-dependent changes.
Development: Adjust immature losses to their ultimate levels.
Loss Adjustment Expenses (LAE): Load rates for the costs of adjusting claims.
Profit and Contingencies: Add a load for the target profit and risk margin.
Reinsurance Costs: Account for the net cost of reinsurance.
Credibility: Blend the insurer’s experience with complementary data if the volume is low.

Key Concepts and Practical Considerations

Residual Markets

Definition: A safety net for insureds who cannot obtain coverage in the voluntary (standard) market.
Assessment: Risky individuals or deficits are typically assigned or assessed to insurers based on their market share (e.g., an insurer with a $20\%$ market share is assigned $20\%$ of the residual market risks or deficits).
State Differences: Residual market mechanisms and rate adequacy vary by state. If State X has less adequate residual market rates than State Y, standard insurers in State X may face higher assessments.

External Influences Justifying Rate Differences between States

Rates may differ significantly between states (e.g., State X having higher rates than State Y) due to:

Judicial Environment: Higher tendency for lawsuits or larger court awards in certain jurisdictions.
Regulatory and Legislative Differences: Mandatory coverage limits or benefit levels may be higher.
Guaranty Fund Assessments: Differences in how guaranty funds are managed or higher insolvency rates in a state.
Economic Variables: Differences in repair costs, medical costs, or wages affecting claim severities.
Residual Market Deficits: Higher assessments from underpriced residual markets.
Premium Taxes: Differences in state-mandated premium tax rates.
Weather and Geography: Differences in exposure to natural catastrophes (e.g., wind, hail, earthquake).

Catastrophe Coverages (e.g., Terrorism)

When rating for low-frequency, high-severity events:

Include a specific catastrophe provision in the rate indication.
Reflect reinsurance costs and availability.
Consider government backstops (e.g., TRIA) and how they mitigate risk.
Account for increased volatility via a higher profit margin or risk load.
Ensure the rate reflects changes in policy coverage clauses or exclusions.

Premium Trending: Even after adjusting for specific rate changes, the average premium per exposure can change over time due to a changing mix of business (e.g., policyholders shifting to higher deductibles, buying different limits, or changes in the distribution of high- and low-risk insureds). Premium trending accounts for this gradual drift.
Exposure Trending: If the exposure base is inflation-sensitive (e.g., payroll for Workers’ Compensation, sales for General Liability), the exposures themselves must be trended to reflect the values expected in the future prospective period.
Prospective Period: The future policy period for which the rates are being determined.

Rationale for One-Time Premium Adjustments (On-Leveling)

Historical premiums must be adjusted to the current rate level (on-leveled) so that the experience period premium reflects the revenue that would have been generated if current rates had been in effect throughout. Failure to on-level leads to distorted indications:

Example: Consider three experience years: 2024 (Premium = $X$ ), 2025 (Premium = $Y$ , with a $+10\%$ rate change mid-year), and 2026 (Premium = $Z$ ). The prospective period is 2027.
With Adjustment: Adjusting historical premiums to the current rate level yields on-leveled premiums (e.g., $1.10X + 1.05Y + Z$ ). If the resulting loss ratio is $\dfrac{L}{1.10X + 1.05Y + Z} = 65\%$ , the rates are adequate.
Without Adjustment: Using raw premiums ( $X + Y + Z$ ) leads to an artificially low premium base, yielding an artificially high loss ratio (e.g., $\dfrac{L}{X + Y + Z} = 70\%$ ). This would lead the actuary to incorrectly indicate a rate increase when current rates may already be adequate.

*[FIE]: Fundamental Insurance Equation